Chrono Cross: Being my first RPG(besides a Digimon game, anyway), this game really left an impression on me and set the standard for what I expect out of a game. This game has it all: interesting party members(Glam rockstars, androids, French jesters, shapeshifting old ladies, and more) beautiful background art, a unique and fun battle systems, a great story, evil furry overlords. This game was the tits.

Final Fantasy IX: I remember when I first saw this game when I was like 9, I didn't care for it much because it wasn't Chrono Cross. I was wrong. A great cast(including a rat with a spear, a Lickitung wearing a chef hat, and SSJ4 tranny Hitler) in a super interesting world, a cool bestiary, I think this game was a great introduction to the series for me. The cartoony aesthetic works well, too.

Shinobi(PS2): Probably the first super violent game I have ever played, this game ruled. It rewards you for how quickly you kills your enemies, and punishes you if you take too long. Add the difficult platforming, and this game is hard as balls. The good kind of difficultly. Add all of the extra content and you have much replay value.

Legacy of Kain is my all-time favorite series, and Soul Reaver 2 is pribably my favorite of the series. Since that's where the story really reaches its peak. Gameplay-wise, Defiance is probably the best, though.

For fighting games, Mortal Kombat Trilogy has a special place in my heart as the first game I ever owned, and it still plays very well today. Also, KOF 95 for Gameboy was the first ever game I beat and introduced me to the series, of which I'd say 98 is still my favorite.

Turok: Dinosaur Hunter is another one of the first games I ever owned, and still one of the best shooters with its ridiculous, over-the-top guns and enemies.

Those are the ones that immediately come to mind, though there are obviously more. I might come back and amend this post.